Question

How many real solutions if any, does 2x^2-3x+8=0​

Answer 1

The quadratic equation
`2\, x^(2) - 3\, x + 8 = 0` has no real solution.

Explanation:

Rewrite the quadratic equation
`2\, x^(2) - 3\, x + 8 = 0` in the standard form
`a\, x^(2) + b\, x + c = 0`:

`2\, x^(2) + (-3)\, x + 8 = 0`, for which:

• 
  `a = 2`.
• 
  `b = (-3)`.
• 
  `c = 8`.

The quadratic discriminant of
`a\, x^(2) + b\, x + c = 0` is
`(b^(2) - 4\, a\, c)`. The quadratic discriminant of
`2\, x^(2) + (-3)\, x + 8 = 0` would be:

`\begin{aligned}& b^(2) - 4\, a\, c \\ =\; & (-3)^(2) - 4 * 2 * 8 \\ =\; & (-55)\end{aligned}`.

Since the quadratic discriminant of this equation is negative, this quadratic equation has no real solution.